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Based on what I have read, I know that finished compost is about half in volume if done by cold composting rather than by hot composting. What is the reason for this? Is it just much more dense? Would that mean that a cubic foot of compost which has been cold composted would be much higher in nutrients than an equal amount made from the same materials which have been hot composted?

I suspect it is because cold composting rots down over a much longer time than hot composting and the liquids produced often run out the rotting material

Hot composting is a more controlled exercise , your just aiming to get the bacteria to the stage of using the nitrogen in the heap used up till they then start making there own and the material being composted to also start releasing the other locked in nutrients etc . Then by almost dessicating things you hold the nutrients in place till you transfer the hot compost to the garden .

Re the amount of nutrients cubic foot for cubic from what I have read ( makes sense as well ) the longer the rotting \& liquid run off takes place there will be less of them in the cold composted material

You could perhaps use a barrel with the top cut off and make a simgle small drain hole in the base to drain out the liquid stuff for use as a liquid feed if you dilute it first . However this idea is hard work and it takes years for the material to fully rot down as it tends to turn black and smelly due to the oxygen being used up in the first few months .( Anerobic composting )

In late Feb this year I uncoverd the bags and found the top stuff reasonably dry but the lower half was heavy and soggy .

I decided to use up six bags to add to the existing composting bins which were about 2/3 full after settling down over the winter .

I had to use the sack barrow to move the sacks and had to use a box cutter knife to slice open the sacks . I confess to vomiting because of the stink of the lamb shed stuff & that from the turkey shed . Every lower half of the bags contents had gone black/ dark green , thick and slimey .. Her next door was non too chuffed either for it took three days for the stench to dissipate, despite me incorporating it into four of my Dalek composters as I turned them over.